Best ever?

For me, that would have to be a running coyote pup at 125 yards with a S&W 6" Mod 19! It was the fifth round that finally connected, but as my witness stated, "You were shooting "at" him!". Which I think meant, "Yeah, I know "luck" when I see it!" But it DID happen.
Last deer season, sitting in my blind, I saw three deer. One crawled under the fence. I've got a bench and sand bags. When she stopped to graze, I saw her fall in the scope and another deers feet fly across the top of the sight picture. By the time I reloaded my Ruger No. 1, the second doe was at 175 yards standing broadside. I watched her drop in the scope.
Total elapsed time? I'd say 8 to 10 seconds and my doe season was over!
I could have shot the third but jiminy cat whiskers! Two's enough!

I shot a 30 inch mule deer in Colorado at 400 yards. It took 2 shots but I finally settled down on the second shot a made it count.

Mule deer at about 400 yards one more step and he was gone.

I am not sure about best shots, but 65 plus years of hard hunting have resulted in some lucky shots

52" Bull Moose at 262 yards. Two shots, were 1 1/2" apart, fired from a .338 win mag free standing. A friend on the hunt rewarded myself and my father with great shooting when he investigated the POI's on the moose. He had assumed that we both shot because the sound of the repercussions were so close together. That is when my father informed him that he never even pulled the trigger, and informed me that he didnt realize i shot twice. I couldnt tell you an actual time in between shots, or exactly why i shot twice, all i remember is that the bull stumbled and started to rise, so i hit him again. It was down hill and the sun had just set, and I didnt want him getting into the woods line. Other than that, i once shot three woodies with two shots, bang bang limit. One of the woodies landed in the conoe with us and hit my paddler in the jimmies. Id rather be luck than good... whatever that means.

I was varminting for woodchuck not far from Oneonta-Delhi, NY and the grass was too tall to take the shot in the prone, sitting or kneeling position, so I had to take it in the standing offhand position with a heavy-barreled .222 and a 12X scope. I could see my pulse in the crosshairs and that rifle was decidedly muzzle-heavy! I squeezed it off and even I was surprised to solidly connect. I doubt I could do that at the same distance today!

I have never made a bad kill shot. The best shot I will ever make will be my last. Too many variables to consider with this question. I have made shots on running deer that died standing upright between 2 trees where it was shot. I have shot ground hogs at 575 yards and red squirels with the bow at 25 yards through the neck. What is truely your best shot. The one that gets the job done the fastest and humanly. There is a saying. "Even A Blind Pig Finds an Acorn Once In A While" Meaning, even the very worst can get the job done once in a while , while the very best can be the very worst any given day.

My best shot would have to be this one: I saw a doe walking out of the field I was hunting. She was about 100 yards away. I shot and missed. I stood (I had been needing down) up thinking better go look for blood trails (I didn't know I had missed yet). Once I stood up for some unknown reason I put another bullet in the chamber. I never do that. Anyway, I hadn't taken a single step before the deer jumped out of the woods and ran all the way across the field to about 50 yards up the edge of the woods I was standing next to. Once I had see the deer come out of the woods, I had been trying to line up another shot. I have to admit, the deer did stop on the edge of the woods, but the second it did I shot it, off hand, right at dark, moving (almost) target. I made that shot. I had never practiced off hand shooting with a scoped rifle before. Now, it was a bit of a gut shot, but not bad for a first off hand shot ever.